Question

A random sample of n = 25 is obtained from a population with variance ² , and the sample mean is computed to be  = 70. Consider the null hypothesis H0 :  = 80 against H1 :  < 80 and compute the p-value when ² = 600.

Answer 1

Given,

n = 25

X_bar = 70

² =600

Hypothesis :

H₀: =80

H₁: < 80

First calculate test statistic value

= ² = 600 = 24.49

t= (x_bar - ​​​​​​) /(/n)

= (70-80)/(24.49/25)

t = - 2.042

Calculate df

Df =n-1 = 25-1 = 24

P value for t test statistic with 24 degree of freedom is 0.0262.

P value = 0.0262